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Euler's Totient Function on Odd and Even Natural Numbers

Recall from the Euler's Totient Function page that if $n \in \mathbb{N}$ then $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$. The function $\phi$ is called Euler's totient function.

We will now look at two very simple and nice properties of the Euler totient function.